On Simultaneous Percolation with Two Disk Types

TL;DR

This paper analyzes the conditions under which two different Gilbert disk models can simultaneously percolate without interference, providing insights into the coexistence of two cognitive radio networks.

Contribution

It characterizes the density regions allowing both models to have a unique infinite component under exclusion constraints, a novel analysis for coexisting networks.

Findings

Identifies density regions for simultaneous percolation.

Provides conditions for coexistence of two disk models.

Offers theoretical insights into cognitive radio network coexistence.

Abstract

In this paper we consider the simultaneous percolation of two Gilbert disk models. The two models are connected through excluding disks, which prevent elements of the second model to be in the vicinity of the first model. Under these assumptions we characterize the region of densities in which the two models both have a unique infinite connected component. The motivation for this work is the co-existence of two cognitive radio networks.